Collective Dynamics on a Two-Lane Asymmetrically Coupled TASEP with Mutually Interactive Langmuir Kinetics

Motivated by the recent experimental observations on clustering of motor proteins on microtubule filament, we study an open system of two parallel totally asymmetric simple exclusion processes under asymmetric coupling conditions, which incorporates the mutual interaction with the surrounding environment through Langmuir Kinetics (LK) in both the lanes. In the modified LK, the attachment and detachment rates depends on the configuration of nearest neighboring sites. We analyse the model within the framework of continuum mean-field theory and the phase diagrams along with density profiles are obtained using boundary layer analysis. The effect of mutual interactions on the phase diagram for two different situations of attachment and detachment (LK) rates is discussed. Under the symmetric LK dynamics, the topological structure of the phase diagram remains similar to the one in without mutual interaction; while for the antisymmetric case, after a certain critical value of attractive/repulsive mutual attraction, significant changes are found in the qualitative nature of phase diagram. Moreover, it is shown that the type of mutual interaction affects the dynamic properties of motor proteins. The theoretical findings are examined by extensive Monte-Carlo simulations.